The embarrassing admission follows a landmark private prosecution by local fisherman Ian Cook, who discovered hundreds of poisoned salmon, trout and eel washed up near the site.
It is the first time the agency has been prosecuted since it was formed a decade ago.
In Cullompton magistrates' court, the agency and its contractor May Gurney admitted a charge under the Salmon and Freshwater Fisheries Act of allowing polluting matter to enter a stream.
After the hearing, Cook, who owns fishing rights on the Exe, said the agency had not come out 'smelling of roses'.
He added that it was 'appalling' that he had to take legal action against the agency and a national construction firm working for it.
'We put faith in the agency to bring a prosecution against themselves and the contractors, but this did not happen,' Cook said.
Adjourning sentencing until 10 May, chairman of the bench Sarah Fry said this was one of the worst recorded incidents of river pollution.
'This causes enormous public concern given the EA is the watchdog for upholding standards,' she added.
Both EA and May Gurney declined to comment.